This paper provides a discussion of methodological issues relating to the estimation of the long-run relationship between exchange rates and fundamentals for Central and Eastern European acceding countries, focusing on the so-called behavioural equilibrium exchange rate (BEER) approach. Given the limited availability and reliability of data as well as the rapid structural change acceding countries have been undergoing in the transition phase, this paper identifies several pitfalls in following the most straightforward and standard econometric procedures. As an alternative, it looks at the merits of a two-step strategy that consists of estimating the relationship between exchange rates and economic fundamentals in a panel cointegration setting - using a sample which excludes acceding countries - and then "extrapolating" the estimated relationships to the latter. While focusing on the first step of such a strategy, the paper also delves into discussing technical aspects underlying the "extrapolation" stage. As a result, the paper endows the reader with the methodological and empirical ingredients for computing equilibrium exchange rates for acceding countries, providing estimates for the long-run coefficients between real exchange rates and economic fundamentals and a discussion of how to apply these results to acceding countries data.